# How Fourier Synthesis is performed using Matlab ?

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ramdas patil on 18 May 2015
Commented: Ahmed Mujtaba on 16 Nov 2016
http://whatis.techtarget.com/definition/Fourier-synthesisFourier-synthesis I want to clear my concept about Fourier Synthesis using Matlab .But don't know how to do this.
So can anybody show me how Fourier Synthesis is performed using Matlab?

Youssef Khmou on 18 May 2015
Edited: Youssef Khmou on 18 May 2015
Fourier synthesis is simple application of coefficients summation either numerically or symbolically, Fourier decomposition requires certain conditions of the input function, you can start with a simple example which is an approximation of a square wave of 2 Hz, using 11 terms :
Fs=150;
t=0:1/Fs:4-1/Fs;
f=2;
x=square(2*pi*f*t);
figure;
plot(t,x);
axis([0 1 -2 2]);
% Approximation with Fourier decomposition
y=0;
N=11;
for r=1:2:N
y=y+sin(2*pi*f*t*r)/r;
end
hold on;
plot(t,y,'r');
xlabel('t');
ylabel('magnitude');
hold off;
Ahmed Mujtaba on 16 Nov 2016
Thanks.. Exactly what I was looking for. Simple and Compact.

Image Analyst on 18 May 2015
There is nothing at that link. I don't know what Fourier Synthesis might be synthesizing. I don't think computing the Fourier spectrum of a signal or image is called "synthesizing", at least not by anyone I know, so I'm not really sure. You can synthesize things though, such as the attached demo where I synthesize clouds by manipulating the Fourier Spectrum.
Image Analyst on 19 May 2015
Make sure that you're passing in an even number for rows and columns.

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